Set cover problem has some well-known bounds relating the size of a set cover and the frequency of element covered[1]}, [2]}.
[[1]}, [2]}]
Let there be a collection of \(t\)  sets each with size at most \(a\) , and each element of the universe is covered by at least \(b\)  of the sets, then there exists a subcollection of \(O(\frac{t}{b}\log a)\)  sets that covers the universe.
